Superconductive Contour with Inductance and Magnetic Field: Current Calculation

[cdummie]

1. The problem statement, all variables and given/known data
We have a superconductive contour in the shape of circle with radius $a$. Inductance of contour is $L$, when the contour is out of magnetic field, there's no current in it. What's the current in the contour when constant magnetic induction vector appears in it, if magnetic induction vector is normal( 90 deg.) to the plane of contour.

Homework Equations

The Attempt at a Solution

Few things here are not clear to me, i mean, current should be $i(t)=\frac{e(t)}{R}$, but since contour is superconductive then i suppose that resistance should be zero. Now, next thing is $e(t)$. How many there are sources of induced electric field? How can i find them? Is there only self-inductance present in this system?

 

[gneill]

The Attempt at a Solution

Few things here are not clear to me, i mean, current should be $i(t)=\frac{e(t)}{R}$, but since contour is superconductive then i suppose that resistance should be zero. Now, next thing is $e(t)$. How many there are sources of induced electric field? How can i find them? Is there only self-inductance present in this system?

I'm not positive about this, but I think that you can apply Lenz's law to obtain the direction of the induced current, and assume that the superconductor can generate, without opposition from resistance, any current necessary to oppose (cancel) the external field within the loop. So maybe invoke the Biot-Savart law to find an appropriate current?